| Summary: | Delivery service sharing (<b>DSS</b>) has made an important contribution in the optimization of daily order delivery applications. Existing DSS algorithms introduce two major limitations. First, due to computational reasons, most DSS algorithms focus on the fixed pickup/drop-off time scenario, which is inconvenient for real-world scenarios where customers can choose the pickup/drop-off time flexibly. On the other hand, to address the intractable DSS with the flexible time windows (<b>DSS-Fle</b>), local search-based heuristics are widely employed; however, they have no theoretical results on the advantage of order sharing. Against this background, this paper designs a novel algorithm for DSS-Fle, which is efficient on both time complexity and system throughput. Inspired by the efficiency of shareability network on the delivery service routing (<b>DSR</b>) variant where orders cannot be shared and have the fixed time window, we first consider the variant of DSR with flexible time windows (<b>DSR-Fle</b>). For DSR-Fle, the order’s flexible time windows are split into multiple virtual fixed time windows, one of which is chosen by the shareability network as the order’s service time. On the other hand, inspired by efficiency of local search heuristics, we further consider the variant of DSS with fixed time window (<b>DSS-Fix</b>). For DSS-Fix, the beneficial sharing orders are searched and inserted to the shareability network. Finally, combining the spitting mechanism proposed in DSR-Fle and the inserting mechanism proposed in DSS-Fix together, an efficient algorithm is proposed for DSS-Fle. Simulation results show that the proposed DSS-Fle variant algorithm can scale to city-scale scenarios with thousands of regions, orders and couriers, and has the significant advantage on improving system throughput.
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